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A325713
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Number of separable partitions of n in which the number of distinct (repeatable) parts <= 4.
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1
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1, 1, 2, 3, 5, 6, 10, 14, 19, 26, 37, 49, 66, 87, 115, 150, 193, 244, 309, 387, 479, 585, 714, 860, 1032, 1226, 1454, 1697, 1991, 2304, 2672, 3060, 3518, 3981, 4541, 5121, 5782, 6462, 7265, 8057, 9000, 9938, 11031, 12131, 13384, 14634, 16085, 17534, 19161
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OFFSET
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1,3
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COMMENTS
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A partition is separable if there is an ordering of its parts in which no consecutive parts are identical. See A325534 for a guide to related sequences.
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LINKS
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MATHEMATICA
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(separable=Table[Map[#[[1]]&, Select[Map[{#, Quotient[(1+Length[#]), Max[Map[Length, Split[#]]]]}&, IntegerPartitions[nn]], #[[2]]>1&]], {nn, 35}]);
Map[Length[Select[Map[{#, Length[Union[#]]}&, #], #[[2]]<=4&]]&, separable]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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